Finite Group DatabasebetaFinite Group Databasebeta| order | 13568 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #392 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C42×C53 · Schur multiplier (H2) = C23 |
| direct product | C53×#8135 |
| subgroup | G/H | |
|---|---|---|
| center | C2×C42×C53 | C23 |
| commutator | C23 | C2×C42×C53 |
| Frattini, cosocle | C2×C42 | C23×C53 |
| socle, prime radical | C23×C53 | C2×C42 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C2×C42×C53 ◁ G | |
382 conjugacy classes of subgroups.
| minimal degree | μ(G) = 93 |
| transitive degree | μt(G) = 13568 |
A minimal faithful permutation representation — 3 generators on 93 points:
(1,2)(3,6)(4,5)(7,8)(9,10,12,16,13,15,19,22)(11,14,18,20,17,21,23,24)(25,26)(27,30)(28,32)(29,31)(33,37)(34,36)(35,38)(39,40)(41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93);(2,5)(6,8)(9,11)(10,14)(12,18)(13,17)(15,21)(16,20)(19,23)(22,24)(25,27,28,33,29,34,35,39)(26,30,32,37,31,36,38,40);(1,3,4,7)(2,6,5,8)(10,15)(11,17)(16,22)(18,23)(26,31)(30,36)(32,38)(37,40)4664 conjugacy classes. The character table is too large to display.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(13568, 1123);